Math Is Fun Forum

LuisRodg

Real Member

Registered: 2007-10-23

Posts: 322

Whats convention on digits accuracy?

Im just brainstorming here.

Lets say i have the following two numbers:

2.31
2.39

How many digits are they accurate to? 1 or 2? So basically, for accuracy do you go to the decimal digits to check how many digits match? (so in this case it will be accurate to 1 digit?)

Thanks.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Whats convention on digits accuracy?

Hi LuisRodg;

I am not sure you are asking the right question. In numerical work when you write 2.31 you are implying an error of ± .005

Actually every number is really not a number but an interval. You are saying that the number is between 2.305 and 2.315

If those two numbers were the result of some numerical calculation that we hoped was converging on a value then it is common to take the digits that agree. So it would be 2.3. Although that would be extremely weak numerical work.

For instance, supposing we want to numerically sum this.

We could say:

We would use the digits that agree as an estimate of the sum.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Whats convention on digits accuracy?

hi LuisRodg

How many digits are they accurate to? 1 or 2? So basically, for accuracy do you go to the decimal digits to check how many digits match? (so in this case it will be accurate to 1 digit?)

To 1 dp the numbers you suggest, 2.31 = 2.3 (1dp)  and 2.39 = 2.4 (1dp) so bizarrely, they don't even agree at 1dp.

As bobbym says, when you give a number, the number of dp implies the accuracy to which you know the number.

So giving a number as 2.31 means it could be anything in the range 2.305 to 2.315

and for 2.39 it could be anything in the range 2.385 to 2.395.

Notice these ranges do not overlap.

A lot depends on context.

If a question says: The radius of a circle is 3.5 cm what is its area?  MS Excel says the result of my calculation is 38.484510006475, but it would be silly to state the answer with those many digits.

But allowing that the radius might really be as low as 3.45 the result is 37.3928065593525
and if I use 3.55 I get 39.5919214168654

Surprisingly, these results don't even agree in the units digit.

The advice I give to exam students is (i) use common sense about how accurately you give an answer and (ii) never give more (significant) digits than the least accurately known number in the calculation.

I think the answer to your original question is 1.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
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John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Whats convention on digits accuracy?

Sort of on this discussion, but a little bit of
trivia a little off the subject is how IUPAC
is describing the atomic weights of the
elements now, since 2010.
Here are your 2 numbers as IUPAC would
describe them; there are two ways that
are being used, depending on the chemical
elements.  At this time, ten elements use
the range technique with square brackets,
and about 74 other elements use the middle
number with a plus/minus value in parenthesis
at the end of the number as shown below:
2.35(4)
[2.31; 2.39]
I figured this bit of trivia might be helpful
to someone, never know.

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